The invention relates to a method of reconstructing three-dimensional images from cone beam projection data of an object to be examined which is arranged in an examination zone, and also relates to a corresponding X-ray device.
For the imaging in an X-ray device, for example a C-arm system, in principle a set of cone beam projection data is acquired first from the part of an object to be imaged and the three-dimensional distribution of the X-ray attenuation coefficient within the part of the object to be imaged can subsequently be reconstructed therefrom. This distribution then serves as a 3D image of this part of the object to be examined, that is, of the so-called examination zone. In the case of medical applications the object to be examined is usually a human body. The cone beam used for the projection is formed by a substantially punctiform X-ray source (the apex of the cone) and the sensitive surface of the X-ray detector (the base of the cone) which is possibly reduced by diaphragms. The examination zone of the object to be examined is then situated between the X-ray source and the X-ray detector. The X-ray source and the X-ray detector in a commonly used isocentric C-arm system are connected essentially rigidly to one another, the connecting line between the X-ray source and the center of the X-ray source always passing more or less exactly through the isocenter.
The position of the X-ray source, and hence the orientation of the cone beam, can be chosen at random within given limits which are imposed by the construction. In order to acquire a set of cone beam projection data, the X-ray source is displaced along a predetermined trajectory around the examination zone to be imaged, one cone beam projection after the other being measured at short intervals in time or in space during said displacement. Because of the construction, the trajectory is situated at least approximately on the surface of a sphere whose center is formed by the isocenter of the C-arm system.
For a predetermined trajectory C-arm systems of this kind have a spherical volume having the following three properties: the center of the spherical volume is formed by the isocenter; the spherical volume is covered by all cone beams whose apex is situated on the trajectory; the spherical volume is the largest sphere having both these properties. The diameter of this sphere hardly depends on the choice of the trajectory, but is highly dependent on the dimensions of the detector and some other geometrical parameters. In practice the diameter is between 20 and 30 cm. Because a human body does not fit into such a small sphere, the cone beam projections are necessarily cut off, meaning that the cone beam does not cover the entire body.
When the trajectory is suitably chosen, each plane which intersects the sphere also intersects the trajectory. A trajectory having this property is often also referred to as being complete in relation to this sphere. Suitably constructed C-arm systems are capable of realizing trajectories which are complete in relation to the sphere. Thus, if the trajectory were complete in relation to the sphere and the projections were not cut off, the image of the part of the object to be examined which is situated within the sphere would be unambiguously determined by all cone beam projections along the trajectory. Using a suitable reconstruction algorithm, the image determined in these circumstances could be reliably and accurately reconstructed within the sphere. Such a reconstruction algorithm is disclosed, for example, in the article xe2x80x9cA cone beam reconstruction algorithm using shift-variant filtering and cone-beam backprojectionxe2x80x9d, Defrise, M. and Clack, R., IEEE Transactions on Medical Imaging, Vol. 13, No. 1: pp. 187-195, March 1994.
Granted, in practice the trajectory can be configured in such a manner that the condition of completeness is satisfied. The fact that cone beam projections are cut off, however, is inevitable at least for most applications. Consequently, the image of the part of the object to be examined which is situated within the sphere can no longer be unambiguously determined, not even when the trajectory is complete. The true image is to be considered rather as the sum of two images, the first of which is unambiguously determined by the measured components of the cone beam projections and can also be calculated. The second image could also be unambiguously determined by the cut-off components of the cone beam projections, but cannot be calculated because exactly these components of the cone beam projections are missing.
U.S. Pat. No. 5,640,436 discloses a method of continuing cut-off cone beam projections in computed tomography. The trajectory is then formed as a circular path. According to this method it is proposed to continue the cone beam projection data beyond the edge zone, that is, parallel to the plane of the circular path and into an outer zone and to reconstruct images from the continued projections, one-dimensional filtering being performed along the continued lines during the reconstruction.
The one-dimensional continuation can be carried out, for example, by means of a method which is described in the article xe2x80x9cProcessing of incomplete measurement data in computer tomographyxe2x80x9d, R. M. Lewitt, Medical Physics, 6 (5): pp. 412-417, 1979.
It is an object of the present invention to provide a reconstruction method of the kind set forth which enables the formation of high-quality three-dimensional images of the desired examination zone also from cut-off cone beam projection data. This object is achieved by means of a reconstruction method of the kind set forth which includes the following steps:
a) acquiring the cone beam projection data by means of an X-ray device which includes an X-ray source and an X-ray detector, the X-ray source being displaced along a trajectory around the examination zone in order to acquire the projection data,
b) determining the contour of the sensitive detector surface of the X-ray detector on which the projection data was acquired,
c) determining pseudo-projection data in an overall outer zone, enclosing the sensitive detector surface in an annular fashion, from the projection data acquired, and
d) reconstructing a three-dimensional image of the examination zone from the projection data acquired on the sensitive detector surface and from the pseudo-projection data determined in the outer zone.
The method in accordance with the invention is based on the recognition of the fact that the described second image, which would be determined by the cut off components of the cone beam projections varies only little and comparatively smoothly inside the spherical volume determined by all cone beam projections. In the vicinity of the edge of the spherical zone, however, it may vary more strongly. A coarse estimate of the cut off components of the cone beam projections would already enable calculation of a usable approximation of this second image within the spherical volume.
The invention utilizes the above insight and hence proposes to supplement in a first step the cut off cone beam projections detected on the sensitive detector surface in such a manner that they may be considered approximately as projections of an imaginary object to be examined which have not been cut off, said object to be examined being situated completely within a larger spherical volume. In order to continue the cut off projections, pseudo-projection data should thus be determined in an outer zone which is filled completely and preferably as uniformly as possible. The larger spherical volume is then chosen to be significantly larger than the former, smaller spherical volume, being the so-called inner zone, but is preferably situated around the same center. The imaginary object to be examined arises from the actual object to be examined by omission of all parts situated outside the larger spherical volume. Furthermore, in accordance with the invention it is proposed to reconstruct in a second step the desired image of the part of the object to be examined which is present within the smaller spherical volume from the supplemented cone beam projections derived during the first step, that is, from the cone beam projection data acquired within the smaller spherical volume and from the pseudo-projection data acquired in the so-called outer zone, that is, the difference volume between the larger and the smaller spherical volume.
A suitable reconstruction algorithm is, for example, once more the algorithm described in the article by Defrise and Clack.
A three-dimensional image reconstructed by means of the method in accordance with the invention deviates from the true image of the part of the object to be examined which is present in the smaller spherical volume, that is in the inner zone, merely in the form of an unknown, but very weak, smooth and almost constant image which varies only to a comparatively small extent, that is, even in the vicinity of the edge of the inner zone. The reconstructed image thus enables the recognition of fine anatomical details, but does not provide absolute numerical values of the X-ray attenuation coefficient. When the image reproduces an organ whose attenuation coefficient is known, however, the image can be normalized afterwards by addition of a suitable constant.
The method in accordance with the invention can also be used when the trajectory is not complete in relation to any sphere; this is the case when the trajectory consists of a circle or a part of a circle. The so-called algebraic reconstruction technique can always be used as the reconstruction algorithm; in the case of a (partial) circle it is also possible to use the known Feldkamp, Davis and Kress algorithm. Generally speaking, in such a case the reconstructed image will contain additional artefacts which are due to the failure to meet the condition of completeness. It is to be noted, however, that the reconstruction can also be limited to a sub-volume of the inner zone.
Preferably, the outer zone is chosen in such a manner that it covers at least a significant part of each cone beam projection of the object to be examined which emanates from an arbitrary point of the trajectory.
A further version of the method in accordance with the invention utilizes only the acquired edge projection data, that is, the projection data acquired in the edge zone of the sensitive detector surface, so as to determine the pseudo-projection data in the outer zone. Moreover, pseudo-projection data is preferably determined only on the basis of directly neighboring edge projection data.
A more or less accurate estimate of the appearance of the object to be examined is used for the determination of the pseudo-projection data, that is, the continuation of the cut off cone beam projections. However, it is advantageous to utilize a priori information concerning the appearance of the object to be examined. A comparatively accurate estimate can be made, for example, by means of additional sensors, for example, tactile or optical sensors or ultrasound sensors.
Whereas in accordance with the method proposed in U.S. Pat. No. 5,640,436 the cone beam projections are continued along parallel lines which extend parallel to the trajectory which is assumed to be circular, in conformity with the version of the method of the invention as disclosed in claim 5 it is proposed to continue the cone beam projections along straight, radial lines whose respective point of origin is situated at or near the center of the sensitive detector surface and which lines, therefore, intersect at that area. The desired complete filling of the outer zone with pseudo-projection data is thus achieved on the one hand. On the other hand, reconstruction methods other than the reconstruction method unconditionally specified in said U.S. Pat. No. 5,640,436 can then be used for the formation of three-dimensional images. Overall, a significantly better resolution can thus be achieved for the images.
In the case of the known X-ray detectors the measured projection data lies situated at grid points of a Cartesian system of co-ordinates or, for example, in the case of an image intensifier, of a distorted Cartesian co-ordinate system. In order to carry out the continuation of the cone beam projections along radial lines, therefore, it is advantageous to determine the acquired projection data first in a polar co-ordinate system, for example, to convert the projection data present in cartesian co-ordinates into polar co-ordinates by linear interpolation. The pseudo-projection data can then be determined in polar co-ordinates and subsequently be converted into the cartesian co-ordinate system of the projection data present in the inner zone, for example, by linear interpolation in the angular direction between pseudo-projection data of neighboring lines.
Different approaches can be followed so as to calculate the pseudoprojection data. One possibility consists in continuing the radial variation of the values of the projection data essentially smoothly in the outer zone and letting it decrease to 0 inside the outer zone. To this end, elliptical curves or other simple continuations can be chosen; this already offers an improvement of the image quality. However, it may also be arranged to determine pseudo-projection data along each radial line in conformity with a more complex formula, for example, by application of a first-order polynomial as indicated in claim 10; in that case a plurality of parameters is used, for example, the width of the edge zone wherefrom edge projection data is used, and the length of the object to be examined along the corresponding radial line which is situated within the contour of the larger spherical volume. A comparatively good continuation of the cone beam projections along the individual radial lines can thus be achieved, ultimately leading to a high image quality.
Further advantageous embodiments are disclosed in the indicated dependent claims. The invention also relates to an X-ray device as disclosed in claim 11. In practice such an X-ray device is preferably realized as a C-arm system or as a so-called computed tomography device equipped with a gantry. It is to be noted that the X-ray device in accordance with the invention may be further elaborated in the same or similar way as the method described above.